Use a simulation to test a model, and to compare two treatments

Answer Key - Grade 11 Math Worksheet - Challenge Me

Circle the best answer, or write your answer on the line.

1. 1.

   Kira's class tested two wing designs on 24 paper airplanes, assigned at random. The two group means differ by 3 feet. What share of chance dots are 3 or more from 0, either way?

   0.19
2. 2.

   Luz's class tested quiet versus music while studying, on 24 students assigned at random. The two group means differ by 2 words. What share of chance dots are 2 or more from 0, either way?

   0.18
3. 3.

   Milo's class tested ruler-drop practice on 20 students, assigned at random. The two group means differ by 2 cm. What share of chance dots are 2 or more from 0, either way?

   0.38
4. 4.

   Noah's coin landed tails 5 times in a row in 20 flips. The plot shows each fair run's longest tails streak. Does a fair coin fit, or is it doubtful?

   • Doubtful: 5 tails in a row is too many for a fair coin.
   • It proves the coin is fair.
   • Fits: 22 of 100 fair runs had a streak of 5 or more.

5. Read this first

   Use this

   Dot plot of the longest streak of tails in each of 100 runs of 20 with a fair coin; dots at each streak length: 1: 1, 2: 18, 3: 34, 4: 27, 5: 5, 6: 6, 7: 3, 8: 4, 9: 2.

6. 5.

   Pia's coin landed tails 9 times in a row in 20 flips. The plot shows each fair run's longest tails streak. Does a fair coin fit, or is it doubtful?

   • It proves the coin is unfair.
   • Fits: long streaks always happen by chance, even one this long.
   • Doubtful: only 2 of 100 fair runs had a streak of 9 or more.
7. 6.

   Ren's coin landed heads 6 times in a row in 50 flips. The plot shows each fair run's longest heads streak. Does a fair coin fit, or is it doubtful?

   • Doubtful: 6 heads in a row is too many for a fair coin.
   • Fits: 35 of 100 fair runs had a streak of 6 or more.
   • It proves the coin is fair.
8. 7.

   Tala's number cube rolled 4 sixes in a row in 30 rolls. The plot shows each fair run's longest sixes streak. Does a fair number cube fit, or is it doubtful?

   • Fits: long streaks always happen by chance, even one this long.
   • It proves the number cube is unfair.
   • Doubtful: only 1 of 100 fair runs had a streak of 4 or more.

9. Use this

   Dot plot of 100 chance deals of the 24 results into two groups of 12 (difference in mean words remembered, quiet − music, words, rounded to the nearest 1): -2: 3, -1: 22, 0: 40, 1: 33, 2: 2.

10. 8.

    Ari compared 12 students who chose to study with music and 12 who chose a quiet room. The quiet-room group remembered 2 more words on average. What can Ari conclude?

    • Studying with music made the students remember fewer words.
    • Students who chose quiet remembered more, but the groups chose themselves, so the room may not be the cause.
    • Chance alone explains the difference.
11. 9.

    In Bo's class, 12 students chosen at random practiced a ruler-drop test and 12 did not. The practice group's mean catch distance was 4 cm shorter. What can Bo conclude?

    • It proves practice makes everyone's reactions faster.
    • It shows only a link between practice and catching, not a cause.
    • Practice likely made catches faster for students like these.

12. Use this

    Dot plot of 100 chance deals of the 24 results into two groups of 12 (difference in mean flight distance, long wings − short wings, feet, rounded to the nearest 1): -3: 11, -2: 9, -1: 12, 0: 22, 1: 18, 2: 18, 3: 9, 4: 1.

13. 10.

    Esme compared 12 paper airplanes whose makers chose long wings with 12 whose makers chose short wings. The long-wing planes flew 4 feet farther on average. What can Esme conclude?

    • Long wings made the planes fly farther.
    • Long-wing planes flew farther, but the makers chose the designs, so the wings may not be the cause.
    • Chance alone explains the difference.